Methods of calibrating pressure and temperature transducers and associated apparatus

Abstract

A calibration method provides enhanced accuracy in calibrating outputs of sensors. In embodiments described herein, the outputs of one or more sensors are input to a neural network and the neural network is trained to generate calibrated outputs in response thereto. In one method, the neural network is trained to simulate the output of a known accurate reference sensor in response to input to the neural network of the output of a subject sensor. In another method, the neural network is trained to simulate the output of a known accurate reference sensor in response to input to the neural network of the output of a subject sensor and the output of a second sensor. Additional methods are provided which compensate for changes in a stimulus applied to a sensor, the output which is indicative of another stimulus.

What is claimed is:  
     
       1. A calibration method, the method comprising the steps of: 
       applying an input to a first subject sensor, the first subject sensor input including a series of levels of a first stimulus;  
       generating an output of the first subject sensor in response to the first subject sensor input, the first subject sensor output including a series of uncalibrated measurements of corresponding respective ones of the series of first stimulus levels;  
       inputting the first subject sensor output to a neural network;  
       training the neural network to generate a calibrated output of the first subject sensor; and  
       generating an output of a clock device, the output including a series of individual time indications, and wherein the inputting step further comprises inputting the clock device output to the neural network, with ones of the series of individual time indications being identified with corresponding respective ones of the series of first stimulus levels.  
     
     
       2. A calibration method, the method comprising the steps of: 
       applying an input to a first subject sensor, the first subject sensor input including a series of levels of a first stimulus;  
       generating an output of the first subject sensor in response to the first subject sensor input, the first subject sensor output including a series of uncalibrated measurements of corresponding respective ones of the series of first stimulus levels;  
       inputting the first subject sensor output to a neural network; and  
       training the neural network to generate a calibrated output of the first subject sensor,  
       wherein in the first subject sensor output generating step, the uncalibrated measurements of the series of first stimulus levels are influenced at least in part by changes over time in the first subject sensor input,  
       wherein in the inputting step, the changes over time in the first subject sensor input are input to the neural network by associating each one of the series of uncalibrated measurements of the series of first stimulus levels with a corresponding respective one of a series of relative time measurements generated by a clock device.  
     
     
       3. The method according to  claim 2 , wherein in the training step, the neural network is trained to generate the calibrated output of the first subject sensor which compensates for the influence of the changes over time in the first subject sensor input on the series of uncalibrated measurements of the series of first stimulus levels. 
     
     
       4. A calibration method, the method comprising the steps of: 
       applying an input to a first subject sensor, the first subject sensor input including a series of levels of a first stimulus;  
       generating an output of the first subject sensor in response to the first subject sensor input, the first subject sensor output including a series of uncalibrated measurements of corresponding respective ones of the series of first stimulus levels;  
       inputting the first subject sensor output to a neural network; and  
       training the neural network to generate a calibrated output of the first subject sensor,  
       wherein in the first subject sensor output generating step, the uncalibrated measurements of the series of first stimulus levels are influenced at least in part by changes over time in a series of second stimulus levels,  
       wherein in the inputting step, the changes over time in the series of second stimulus levels are input to the neural network by associating each one of the series of second stimulus levels with a corresponding respective one of a series of relative time measurements generated by a clock device.  
     
     
       5. The method according to  claim 4 , wherein in the training step, the neural network is trained to generate the calibrated output of the first subject sensor which compensates for the influence of the changes over time in the series of second stimulus levels on the uncalibrated measurements of the series of first stimulus levels. 
     
     
       6. A calibration method, the method comprising the steps of: 
       applying an input to a first subject sensor, the first subject sensor input including a series of levels of a first stimulus;  
       generating an output of the first subject sensor in response to the first subject sensor input, the first subject sensor output including a series of uncalibrated measurements of corresponding respective ones of the series of first stimulus levels;  
       inputting the first subject sensor output to a neural network;  
       training the neural network to generate a calibrated output of the first subject sensor,  
       wherein in the first subject sensor output generating step, the uncalibrated measurements of the series of first stimulus levels are influenced at least in part by changes over time in a series of second stimulus levels;  
       applying an input to a second subject sensor, the second subject sensor input including the series of second stimulus levels; and  
       generating an output of the second subject sensor in response to the second subject sensor input, the second subject sensor output including a series of uncalibrated measurements of corresponding respective ones of the series of second stimulus levels,  
       wherein the inputting step further comprises inputting the second subject sensor output to the neural network, and  
       wherein in the second subject sensor output generating step, the series of uncalibrated measurements of the series of second stimulus levels is influenced at least in part by changes over time in the series of first stimulus levels.  
     
     
       7. The method according to  claim 6 , wherein in the inputting step, the changes over time in the series of first stimulus levels are input to the neural network by associating each one of the series of first stimulus levels with a corresponding respective one of a series of relative time measurements generated by a clock device. 
     
     
       8. The method according to  claim 7 , wherein in the training step, the neural network is trained to generate the calibrated output of the second subject sensor which compensates for the influence of the changes over time in the series of first stimulus levels on the uncalibrated measurements of the series of second stimulus levels. 
     
     
       9. A calibration method, the method comprising the steps of: 
       applying an input to a first subject sensor, the first subject sensor input including a series of levels of a first stimulus;  
       generating an output of the first subject sensor in response to the first subject sensor input, the first subject sensor output including a series of uncalibrated measurements of corresponding respective ones of the series of first stimulus levels;  
       inputting the first subject sensor output to a neural network; and  
       training the neural network to generate a calibrated output of the first subject sensor,  
       wherein in the training step, the neural network generates a first output including a series of measurements indicative of corresponding respective ones of the series of first stimulus levels,  
       wherein in the training step, each of the series of measurements in the neural network first output is generated in response to input to the neural network of a selected predetermined quantity of the series of uncalibrated first stimulus level measurements in the first subject sensor output.  
     
     
       10. The method according to  claim 9 , wherein in the training step, the selected predetermined quantity of the series of uncalibrated first stimulus level measurements includes a predetermined quantity of the series of uncalibrated first stimulus level measurements generated prior to the uncalibrated first stimulus level measurement for which each of the series of measurements in the neural network first output is generated. 
     
     
       11. The method according to  claim 9 , wherein in the training step, the selected predetermined quantity of the series of uncalibrated first stimulus level measurements includes a first predetermined quantity of the series of uncalibrated first stimulus level measurements generated subsequent to the uncalibrated first stimulus level measurement for which each of the series of measurements in the neural network first output is generated. 
     
     
       12. The method according to  claim 11 , wherein in the training step, the selected predetermined quantity of the series of uncalibrated first stimulus level measurements further includes a second predetermined quantity of the series of uncalibrated first stimulus level measurements generated prior to the uncalibrated first stimulus level measurement for which each of the series of measurements in the neural network first output is generated. 
     
     
       13. A calibration method, the method comprising the steps of: 
       applying an input to a first subject sensor, the first subject sensor input including a series of levels of a first stimulus;  
       generating an output of the first subject sensor in response to the first subject sensor input, the first subject sensor output including a series of uncalibrated measurements of corresponding respective ones of the series of first stimulus levels;  
       inputting the first subject sensor output to a neural network; and  
       training the neural network to generate a calibrated output of the first subject sensor,  
       wherein in the training step, the neural network generates a first output including a series of measurements indicative of corresponding respective ones of the series of first stimulus levels,  
       wherein in the training step, a series of a selected predetermined quantity of the series of measurements in the neural network first output generated prior to corresponding respective ones of each of the series of measurements in the neural network first output is input to the neural network.  
     
     
       14. The method according to  claim 13 , wherein in the training step, the series of the selected predetermined quantity of the series of measurements in the neural network first output is input to the neural network via a tapped delay line. 
     
     
       15. A method of calibrating first and second sensors, the first sensor generating an output indicative of a first series of levels of a first stimulus applied to the first sensor and influenced by a change in a second series of levels of a second stimulus applied to the first and second sensors, and the second sensor generating an output indicative of the second series of levels of the second stimulus, the method comprising the steps of: 
       time indexing the first and second sensor outputs;  
       inputting the first and second sensor outputs to a neural network; and  
       training the neural network by generating a first output of the neural network corresponding to the first sensor output, utilizing a first tapped delay line to input a first portion of the neural network first output to the neural network, generating a second output of the neural network corresponding to the second sensor output, and utilizing a second tapped delay line to input a second portion of the neural network second output to the neural network.  
     
     
       16. The method according to  claim 15 , wherein the first sensor output includes a series of first uncalibrated measurements corresponding to respective ones of the first series of the levels of the first stimulus, and wherein in the training step, for each one of a series of first measurements included in the first neural network output corresponding to a respective one of the first series of uncalibrated measurements, a first predetermined quantity of the series of the first uncalibrated measurements prior to the respective one of the first series of uncalibrated measurements is input to the neural network. 
     
     
       17. The method according to  claim 16 , wherein in the training step, for each one of the series of first measurements included in the first neural network output corresponding to the respective one of the first series of uncalibrated measurements, a second predetermined quantity of the series of the first uncalibrated measurements subsequent to the respective one of the first series of uncalibrated measurements is input to the neural network. 
     
     
       18. The method according to  claim 17 , wherein the second sensor output includes a series of second uncalibrated measurements corresponding to respective ones of the second series of the levels of the second stimulus, and wherein in the training step, for each one of a series of measurements included in the second neural network output corresponding to a respective one of the second series of uncalibrated measurements, a third predetermined quantity of the series of the second uncalibrated measurements prior to the respective one of the second series of uncalibrated measurements is input to the neural network. 
     
     
       19. The method according to  claim 18 , wherein in the training step, for each one of the series of measurements included in the second neural network output corresponding to the respective one of the second series of uncalibrated measurements, a fourth predetermined quantity of the series of the second uncalibrated measurements prior to the respective one of the second series of uncalibrated measurements is input to the neural network. 
     
     
       20. A method of calibrating a first sensor operatively positionable in a subterranean well, the method comprising the steps of: 
       applying a first sensor input to the first sensor, the first sensor input including multiple levels of a first stimulus;  
       generating a first output of the first sensor in response to the first sensor input;  
       inputting the first sensor first output to a neural network;  
       training the neural network so that the neural network generates a first neural network output which is related to the first sensor input by a first known mathematical function;  
       positioning the first sensor within the well;  
       applying a second sensor input including multiple levels of the first stimulus to the first sensor within the well;  
       generating a second output of the first sensor in response to the second sensor input;  
       inputting the first sensor second output to the neural network; and  
       generating a second output of the neural network which is related to the second sensor input by the first known mathematical function,  
       the positioning step further comprising including the first sensor in a transducer installed in the well,  
       wherein the positioning step further comprises including the neural network in the transducer.  
     
     
       21. The method according to  claim 20 , wherein the positioning step further comprises remotely positioning the neural network relative to the first sensor. 
     
     
       22. A method of calibrating a first sensor operatively positionable in a subterranean well, the method comprising the steps of: 
       applying a first sensor input to the first sensor, the first sensor input including multiple levels of a first stimulus;  
       generating a first output of the first sensor in response to the first sensor input;  
       inputting the first sensor first output to a neural network;  
       training the neural network so that the neural network generates a first neural network output which is related to the first sensor input by a first known mathematical function;  
       applying a second sensor input to a second sensor, the second sensor input including multiple levels of a second stimulus; and  
       generating a first output of the second sensor in response to the second sensor input,  
       the second sensor input applying step further comprising applying the second sensor input to the first sensor along with the first sensor input, and wherein in the-first sensor first output generating step, the first sensor output is influenced at least in part by the second sensor input,  
       wherein the training step further comprises training the neural network so that the first neural network output is compensated for the influence of the second sensor input on the first sensor first output.  
     
     
       23. A method of calibrating a first sensor operatively positionable in a subterranean well, the method comprising the steps of: 
       applying a first sensor input to the first sensor, the first sensor input including multiple levels of a first stimulus;  
       generating a first output of the first sensor in response to the first sensor input;  
       inputting the first sensor first output to a neural network;  
       training the neural network so that the neural network generates a first neural network output which is related to the first sensor input by a first known mathematical function;  
       applying a second sensor input to a second sensor, the second sensor input including multiple levels of a second stimulus; and  
       generating a first output of the second sensor in response to the second sensor input,  
       the second sensor input applying step further comprising applying the second sensor input to the first sensor along with the first sensor input, and wherein in the first sensor first output generating step, the first sensor output is influenced at least in part by the second sensor input,  
       wherein in the first sensor first output generating step, the first sensor first output is influenced at least in part by a change over time of the second sensor output.  
     
     
       24. The method according to  claim 23 , wherein the training step further comprises training the neural network so that the first neural network output is compensated for the influence of the change over time of the second sensor input on the first sensor first output. 
     
     
       25. The method according to  claim 24 , wherein the training step further comprises utilizing at least one tapped delay line to input portions of the first neural network output to the neural network. 
     
     
       26. Apparatus operative in conjunction with a subterranean well, the apparatus comprising: 
       a first sensor generating an output indicative of a series of first stimulus levels applied to the first sensor, the first sensor output including a series of first uncalibrated measurements of corresponding respective ones of the series of first stimulus levels;  
       a neural network generating an output in response to the first sensor output, the neural network output including a series of first calibrated measurements of corresponding respective ones-of the series of first stimulus levels; and  
       a clock device, the clock device time indexing each of the series of first uncalibrated measurements in the first sensor output.  
     
     
       27. Apparatus operative in conjunction with a subterranean well, the apparatus comprising: 
       a first sensor generating an output indicative of a series of first stimulus levels applied to the first sensor, the first sensor output including a series of first uncalibrated measurements of corresponding respective ones of the series of first stimulus levels; and  
       a neural network generating an output in response to the first sensor output, the neural network output including a series of first calibrated measurements of corresponding respective ones of the series of first stimulus levels,  
       wherein the neural network output is compensated for changes in the first sensor output over time.  
     
     
       28. Apparatus operative in conjunction with a subterranean well, the apparatus comprising: 
       a first sensor generating an output indicative of a series of first stimulus levels applied to the first sensor, the first sensor output including a series of first uncalibrated measurements of corresponding respective ones of the series of first stimulus levels; and  
       a neural network generating an output in response to the first sensor output, the neural network output including a series of first calibrated measurements of corresponding respective ones of the series of first stimulus levels,  
       wherein each first calibrated measurement in the neural network output is generated in response to the corresponding respective first uncalibrated measurement in the first sensor output and a first predetermined quantity of prior first uncalibrated measurements, and  
       wherein each first calibrated measurement in the neural network is further generated in response to a second predetermined quantity of first uncalibrated measurements subsequent to the corresponding respective first uncalibrated measurement in the first sensor output.  
     
     
       29. Apparatus operative in conjunction with a subterranean well, the apparatus comprising: 
       a first sensor generating an output indicative of a series of first stimulus levels applied to the first sensor, the first sensor output including a series of first uncalibrated measurements of corresponding respective ones of the series of first stimulus levels; and  
       a neural network generating an output in response to the first sensor output, the neural network output including a series of first calibrated measurements of corresponding respective ones of the series of first stimulus levels,  
       wherein a portion of the neural network output is input to the neural network.  
     
     
       30. The apparatus according to  claim 29 , wherein the neural network output portion is input via a tapped delay line. 
     
     
       31. Apparatus operative in conjunction with a subterranean well, the apparatus comprising: 
       a first sensor generating an output indicative of a series of first stimulus levels applied to the first sensor, the first sensor output including a series of first uncalibrated measurements of corresponding respective ones of the series of first stimulus levels;  
       a neural network generating an output in response to the first sensor output, the neural network output including a series of first calibrated measurements of corresponding respective ones of the series of first stimulus levels;  
       a second sensor generating an output indicative Of a series of second stimulus levels applied to the second sensor, the second sensor output including a series of second measurements of corresponding respective ones of the series of second stimulus levels, wherein the first sensor output is influenced at least in part by the series of second stimulus levels, and wherein the neural network output is generated further in response to the second sensor output.  
     
     
       32. The apparatus according to  claim 31 , wherein the neural network output further includes a series of second calibrated measurements of corresponding respective ones of the series of second stimulus levels. 
     
     
       33. The apparatus according to  claim 31 , wherein the second measurements in the second sensor output are uncalibrated, and wherein the neural network output further includes a series of second calibrated measurements of corresponding respective ones of the series of second stimulus levels. 
     
     
       34. The apparatus according to  claim 33 , wherein the second sensor output is influenced at least in part by the series of first stimulus levels applied to the second sensor simultaneously with the series of second stimulus levels. 
     
     
       35. The apparatus according to  claim 31 , further comprising a clock device, the clock device time indexing each of the series of first uncalibrated measurements in the first sensor output and each of the series of second measurements in the second sensor output. 
     
     
       36. The apparatus according to  claim 31 , wherein the neural network output is compensated for changes in the second sensor output over time. 
     
     
       37. The apparatus according to  claim 31 , wherein each second calibrated measurement in the neural network output is generated in response to the corresponding respective second measurement in the second sensor output and a first predetermined quantity of prior second measurements. 
     
     
       38. The apparatus according to  claim 31 , wherein each second calibrated measurement in the neural network output is further generated in response to a second predetermined quantity of second measurements subsequent to the corresponding respective second measurement in the second sensor output. 
     
     
       39. The apparatus according to  claim 31 , wherein each second calibrated measurement in the neural network output is generated in response to the corresponding respective second measurement in the second sensor output and a predetermined quantity of subsequent second measurements. 
     
     
       40. The apparatus according to  claim 31 , wherein a portion of the neural network output is input to the neural network. 
     
     
       41. The apparatus according to  claim 40 , wherein the neural network output portion is input via a tapped delay line. 
     
     
       42. Apparatus operative in conjunction with a subterranean well, the apparatus comprising: 
       a first sensor generating an output indicative of a series of first stimulus levels applied to the first sensor, the first sensor output including a series of first uncalibrated measurements of corresponding respective ones of the series of first stimulus levels; and  
       a neural network generating an output in response to the first sensor output, the neural network output including a series of first calibrated measurements of corresponding respective ones of the series of first stimulus levels,  
       wherein the first sensor and neural network are interconnected in a transducer.  
     
     
       43. The apparatus according to  claim 42 , wherein the transducer is positioned within the well.